Some prospects for semiproducts and products of modal logics

Valentin Shehtman; Dmitry Shkatov

Some prospects for semiproducts and products of modal logics

Logic 2026-07-20 v1 Logic in Computer Science

Authors: Valentin Shehtman , Dmitry Shkatov

Abstract

We consider products and semiproducts of propositional modal logics L with S5 and present new examples of product and semiproduct logics axiomatized in the minimal way and enjoying the product (or semiproduct) FMP. An essential part of the proof is local tabularity of these (semi)products for L of finite depth; it is obtained by using bisimulation games. These results readily imply decidability for 1-variable fragments of predicate modal logics QL and QL+Barcan formula. We also present new counterexamples, i.e. (semi)products not axiomatizable in the simplest way.

Keywords

modal logic product logic semiproduct logic finite model property local tabularity bisimulation games decidability

Cite

@article{arxiv.2607.17928,
  title  = {Some prospects for semiproducts and products of modal logics},
  author = {Valentin Shehtman and Dmitry Shkatov},
  journal= {arXiv preprint arXiv:2607.17928},
  year   = {2026}
}